GDP/GNP is the only indicator which reflects the working of the whole
economy. The estimates of the GDP/GNP at current and constant prices
provide a firm basis for the measurement of economic growth. To convert
sectors of the GDP/GNP from current to constant and vice versa, various
type of index numbers are used as deflators. Any error in the
computation and use of index numbers will, therefore, effect the
validity of the GDP/GNP.

The use of index numbers for economic analysis is not confined to a
single aspect of the economy. The measurement of dynamic forces and
economic phenomena including the variations in the purchasing power of
money at different points of time owe much to the construction of index
numbers. Due to inherent limitations of various dimensions, index
numbers are criticised as widely as they are used. One of the important
criticism against the use of index numbers for purpose of economic
analysis is that they usually provide result which are not identical
when applied to the same set of data-a situation which bewilders the
users. Even then, index numbers are intensively used though
half-heartedly because there is no tool other than index numbers
available to users. Therefore, an attempt has been made in this paper to
throw light on this proposition and to illustrate the homology of
Laspeyres and Paasche-type index numbers when constructed on the same
set of data.

The main concept of an index number is to measure the general level
of magnitude of group of distinct, but related variables in two or more
situations. Based on this concept, the preparation of index numbers has
a long history and goes back to Edgeworth, who in 1887-89 was Secretary
of a committee of the British Association set up to study methods of
measuring variations in the value of money. Therefore, price indexes,
whether constructed to measure the value of money on different points of
time, or are indexes of wholesale prices, retail prices of agricultural
and manufacturing products etc., all of them are widely used to compare
changes over time and space.

Uses of Index Numbers

The purposes for which index numbers are computed and used are
manifold. Different type of indexes are computed to meet certain needs
e.g. WPI to measure the prices of goods and services sold in bulk, CPI to determine the cost of living etc. Among the main purposes for which
index numbers are computed include the measurement of inflationary
trend, growth rate and real product over time and space.

In most of the developed and developing countries, CPI is also used
for wage adjustment. In US, for example, the construction of CPI was
started during the World War-I when a need was felt to adjust wages with
the high cost of living. Similarly in undivided India, on the
recommendation of the Rau Court of Enquiry in 1944, data on retail
prices were used by the Ministry of Labour to settle a dispute on the
dearness allowance to be given to GIP Railways employees. In Pakistan
too, a start has been made to calculate indexed-pay on the basis of the
trend exhibited by CPI and its effect is given on the wages and salaries
being paid to the employees of the federal and provincial
governments' departments etc. Besides its use for wage-adjustment,
price indexes are also used as deflators for sectors of GNP and flows of
Expenditure on GNP respectively.

Some Basic Criticisms on Index Numbers

Index numbers are generally criticised because they merely reflect
the level of magnitude attained and are indicators of trend only. Since
index numbers suffer from limitation of various types they are simply a
crude device to measure changes in cost and volume of production, trade
and investment at base-year prices. The results obtained by applying
index numbers to certain type of data may not be always close to
reality. Moreover, inconsistent and different results derived from the
same set of data when different type of index numbers are applied to it,
reveal their greatest limitation. The other criticism is that index
numbers usually possess element of bias. For example, at a time when
prices are arising, laspeyres price index usually shows a higher trend
than a Paasche index. This aspect of index numbers is termed as upward
bias in Laspeyres index and downward bias in Paasche index. Fishers
ideal approach to thread a way between the two, is also criticised on he
ground that "the average of two wrong answers does not necessarily
give one right answer.

Homology of Laspeyres and Paasche Index Numbers

The general conclusion that different type of index numbers when
applied to certain data produce results which are not identical. This
fact may not be always true. In certain cases, Laspeyres and Paasche
index numbers are homologous in character and produce symmetric results.
The homology of Laspeyres and Paasche index numbers may be visualized
when the indexes are computed on the basis of same set of data. For
purpose of illustration, different type of indexes have been constructed
which are based on employment and wage data for scheduled banks of
Pakistan for the year 1975-76 to 1979-80. The indexes so computed placed
in Table-I exhibit the homology among each other. Column-2 of Table-I
contains wage data at current prices while Column-5 contains wage data
using 1975-76 average wage; Columns 7 and 8 contain wage indexes based
on Laspeyres and Paasche-type price indexes respectively. Similarly,
employment indexes (Columns 9 and 10) have been computed on the basis of
Laspeyres and Paasche-type volume indexes. The symmetric figures under
Columns-7 and 8 transpire homology of Laspeyres and Paasche indexes.
Similar fact is focused by the figures under Columns 9 and 10.
Therefore, the results (values) derived from the data after deflating
wages at current prices either by Laspeyres and Paasche wage indexes
will also be identical. Similarly, base-year values when extrapolated
either by Laspeyres or Paasche employment volume indexes will be
symmetrical with one another. Since index numbers being identical
whether computed on the basis of Laspeyres or Paasche-type formulae the
results (values) derived from these formulae are coherent showing their
complete homology with one another as given in Columns 5 and 8 of the
Table-2.

Conclusion

Index numbers play a key role in the measurement of inflationary
trend, economic growth and change in cost of living besides their use to
frame economic policies and planning. Therefore, the contributions made
by index numbers for economic analysis cannot be ignored TABULAR DATA
OMITTED though they contain element of various types of errors causing
an equivalent error in the output measurement. Generally, index numbers
are applied to assess the changes occurring in economic activities by
valuing their products. For this purpose, either base-year prices or
price indexes are used as deflators. But in most cases, resort to use
conventional index numbers is usually made instead of constructing index
numbers for specific purposes. Under such circumstances index numbers
not being true representative of the situation fail to yield results
which may be termed real. In order to rectify some of the deficiencies,
it is being suggested that the index numbers be based on the components
of flows involved and they should be directly factored into their own
price and quantity TABULAR DATA OMITTED elements. This process of
constructing index numbers is considered to focus a real picture and
produce better results than one obtained by making indiscriminate use of
conventional index numbers. Furthermore, a great deal of discussion on
the system of national accounts has been made with regard to choice
between Laspeyres and Paasche index numbers and quantity extrapolation and price deflation methods to obtain values at constant prices. Both
Laspeyres and Paasche index numbers as well as extrapolation and
deflation methods work equally well since all of them produce homologous
and symmetrical results. This fact has been illustrated with the help of
the figures given in Table-2 which show the homology of Laspeyres and
Paasche index numbers.

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